Defining an aristotype crystal structure and crystallographic distortions in leucite/pollucite-structured phases with space group $Ia\overline {3} d$

Abstract

A universal aristotype crystal structure for leucite/pollucite-structured phases (A₂B₂^IIIC₄^IVO₁₂, A₂B^IIC₅^IVO₁₂) with space group $Ia\overline {3} d$ has been determined by a non-linear optimisation of the fractional coordinates. The resultant T-site tetrahedron exhibits close to perfect $\overline {4} 3m$ point group symmetry (quadratic elongation 1.0000124, tetrahedral angle variance 1.53 × 10⁻⁵ degrees²). For any distorted leucite/pollucite crystal structure, an associated aristotype phase can be derived from the optimised fractional coordinates, with the aristotype phase lattice parameter calculated from the volume of the hettotype T-site tetrahedron. Assuming the aristotype T-site tetrahedron to be ideal, the distortion of the hettotype tetrahedron from that of the aristotype is described as the linear sum of the amplitudes of an appropriate set of symmetry-adapted basis-vectors of the effective regular TO₄ molecule consistent with the observed point group symmetry within the crystal structure. The methodology is illustrated by reference to the disordered T-site, leucite-structured phase K₂MgSi₅O₁₂.